Wavelets on irregular point sets

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 357, Issue 1760, 1999, Pages 2397-2413

  Daubechies, Ingrid ^a   Guskov, Igor ^a,b   Schröder, Peter ^b   Sweldens, Wim ^c  

^a PRINCETON UNIVERSITY   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c LUCENT TECHNOLOGIES   (United States)

Author keywords

Commutation; Irregular grid; Mesh; Multiresolution; Subdivision; Wavelets

Indexed keywords

EID: 0346876979     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1999.0439     Document Type: Review

References (44)

1. Burt, P. J. & Adelson, E. H. 1983 Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31, 532-540.
2. Catmull, E. & Clark, J. 1978 Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design 10, 350-355.
3. Cavaretta, A. S. & Micchelli, C. A. 1987 Computing surfaces invariant under subdivision. Computer Aided Geom. Design 4, 321-328.
4. Cavaretta, A. S. & Micchelli, C. A. 1989 The desing of curves and surfaces by subdivision algorithms. In Mathematical aspects of computer aided geometric design (ed. T. Lyche & L. L. Schumaker). Tampa, FL: Academic.
5. Cavaretta, A. S., Dahmen, W. & Micchelli, C. A. 1991 Stationary subdivision. Mem. Am. Math. Soc. 93.
6. Chaikin, G. 1974 An algorithm for high speed curve generation. Comp. Graphics Image Process. 3, 346-349.
7. Dahmen, W. 1996 Stability of multiscale transformations. J. Fourier Analysis Appl. 2, 341-361.
8. Daubechies, I. 1988 Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41, 909-996.
9. Daubechies, I. & Lagarias, J. C. 1991 Two-scale difference equations. I. Existence and global regularity of solutions. SIAM Jl Math. Analysis 22, 1388-1410.
10. Daubechies, I., Guskov, I. & Sweldens, W. 1998 Commutation for irregular subdivision. Technical Report, Lucent Technologies, Bell Laboratories.
11. Daubechies, I., Guskov, I. & Sweldens, W. 1999 Regularity of irregular subdivision. Constr. Approx. 15, 381-426.
12. De Boor, C. 1978 A practical guide to splines. Applied Mathematical Sciences, no 27. New York: Springer.
13. de Casteljau, F. 1959 Outillages méthodes calcul. Paris: André Citroën Automobiles SA.
14. de Rham, G. 1956 Sur une courbe plane. J. Math. Pures Appl. 39, 25-42.
15. Deslauriers, G. & Dubuc, S. 1987 Interpolation dyadique. In Fractals, dimensions non entières et applications, pp. 44-55. Paris: Masson.
16. Deslauriers, G. & Dubuc, S. 1989 Symmetric iterative interpolation processes. Constr. Approx. 5, 49-68.
17. Donoho, D. L. 1992 Interpolating wavelet transforms. Preprint, Department of Statistics, Stanford University.
18. Doo, D. & Sabin, M. 1978 Analysis of the behaviour of recursive division surfaces near extraordinary points. Computer Aided Design 10, 356-360.
19. Dubuc, S. 1986 Interpolation through an iterative scheme. J. Math. Analyt. Appl. 114, 185-204.
20. Dyn, N., Levin, D. & Gregory, J. 1987 A 4-point interpolatory subdivision scheme for curve design. Computer Aided Geom. Design 4, 257-268.
21. Dyn, N., Levin, D. & Gregory, J. A. 1990a A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. Graphics 9, 160-169.
22. Dyn, N., Levin, D. & Micchelli, C. A. 1990b Using parameters to increase smoothness of curves and surfaces generated by subdivision. Computer Aided Geom. Design 7, 129-140.
23. Dyn, N., Gregory, J. & Levin, D. 1991 Analysis of uniform binary subdivision schemes for curve design. Constr. Approx. 7, 127-147.
24. Eirola, T. 1992 Sobolev characterization of solutions of dilation equations. SIAM Jl Math. Analysis 23, 1015-1030.
25. Guskov, I. 1998 Multivariate subdivision schemes and divided differences. Technical Report, Department of Mathematics, Princeton University.
26. Guskov, I., Sweldens, W. & Schröder, P. 1999 Multiresolution signal processing for meshes. Computer Graphics Proceedings (SIGGRAPH 99, Los Angeles), pp. 325-334. ACM SIGGRAPH.
27. Heckbert, P. S. & Garland, M. 1997 Survey of polygonal surface simplification algorithms. Technical Report, Carnegie Mellon University.
28. Kobbelt, L. 1996 Interpolatory subdivision on open quadrilateral nets with arbitrary topology. In Proc. Eurographics 96, Computer Graphics Forum, pp. 409-420.
29. Kobbelt, L. 1997 Discrete fairing. In Proc. 7th IMA Conf. on the Mathematics of Surfaces, pp. 101-131.
30. Kobbelt, L. & Schröder, P. 1997 Constructing variationally optimal curves through subdivision. Technical Report CS-TR-97-05, Department of Computer Science, California Institute of Technology.
31. Lane, J. M. & Riesenfeld, R. F. 1980 A theoretical development for the computer generation of piecewise polynomial surfaces. IEEE Trans. Patt. Anal. Mach. Intell. 3, 35-46.
32. Loop, C. 1987 Smooth subdivision surfaces based on triangles. Master's thesis, Department of Mathematics, University of Utah.
33. 2(ℝ). Trans. Am. Math. Soc. 315, 69-87.
34. Micchelli, C. A. & Prautzsch, H. 1987 Computing surfaces invariant under subdivision. Computer Aided Geom. Design 4, 321-328.
35. Reif, U. 1995 A unified approach to subdivision algorithms near extraordinary vertices. Computer Aided Geom. Design 12, 153-174.
36. Rioul, O. 1992 Simple regularity criteria for subdivision schemes. SIAM Jl Math. Analysis 23, 1544-1576.
37. Schröder, P. & Zorin, D. (eds) 1998 Course notes: subdivision for modeling and animation. ACM SIGGRAPH.
38. Schweitzer, J. E. 1996 Analysis and application of subdivision surfaces. PhD thesis, University of Washington.
39. Sweldens, W. 1997 The lifting scheme: a construction of second generation wavelets. SIAM Jl Math. Analysis 29, 511-546.
40. Sweldens, W. & Schröder, P. 1996 Building your own wavelets at home. In Wavelets in computer graphics, pp. 15-87. Course notes ACM SIGGRAPH.
41. Villemoes, L. F. 1994 Wavelet analysis of refinement equations. SIAM Jl Math. Analysis 25, 1433-1460.
42. Warren, J. 1995 Binary subdivision schemes for functions over irregular knot sequences. In Mathematical methods in CAGD III (ed. M. Daehlen, T. Lyche & L. Schumaker). Academic.
43. k continuity of subdivision surfaces. Technical Report, California Institute of Technology.
44. Zorin, D., Schröder, P. & Sweldens, W. 1996 Interpolating subdivision for meshes with arbitrary topology. In Computer graphics (SIGGRAPH '96 Proc.), pp. 189-192. ACM SIGGRAPH.